Question

if a=underoot2 +1 , then find the value of (a-1/a^2)
​

Answer 1

Step-by-step explanation:

Given that,

a=2+

3

Then, Value of

a−

a

1

=2+

3

−

2+

3

1

=2+

3

−

2+

3

1

×

2−

3

2−

3

onrationalize

=2+

3

−

4−3

(2−

3

)

=2+

3

−2+

3

=2

3

Hence, this is the answer

Answer 2

$a = \sqrt{2} + 1 \\ therefore \\ \frac{1}{a} = \frac{1}{ \sqrt{2} + 1 } \\ rationalazing \: the \: \\ denominator \: \sqrt{2} + 1 \\ we \: get \: \\ \frac{1}{a} = \frac{1}{ \sqrt{2} + 1} \times \frac{ \sqrt{2} - 1 }{ \sqrt{2} - 1 } \\ \frac{1}{a} = \frac{ \sqrt{2} - 1}{( \sqrt{2} + 1)( \sqrt{2} - 1) } \\ \frac{1}{a} = \frac{ \sqrt{2} }{ (\sqrt{2} {}^{2}) - ( {1}^{2} ) } \\ \frac{1}{a} = \frac{ \sqrt{2} - 1 }{2 - 1} = \sqrt{2} - 1 \\ therefore \\ a - \frac{1}{a} = ( \sqrt{2} + 1) - ( \sqrt{2} - 1) \\ a - \frac{1}{a} = \sqrt{2} + 1 - \sqrt{2} + 1 = 2 \\ {( \frac{a - 1}{a}) }^{2} = {(2)}^{2} = 4 \\ hence \\ ( { \frac{a - 1}{a}) }^{2} = 4$

Hope it helps u

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